Towards a Generic Trus Model Comparison of Various Trus Updae Algorihms Michael Kinaeder, Erneso Baschny, and Kur Rohermel Insiue of Parallel and Disribued Sysems (IPVS) Universiä Sugar Universiässr. 38 7569 Sugar, Germany {kinaeder, rohermel}@informaik.uni-sugar.de, erns@baschny.de Absrac. Research in he area of rus and repuaion sysems has pu a lo of effor in developing various rus models and associaed rus updae algorihms ha suppor users or heir agens wih differen behavioral profiles. While each work on is own is paricularly well suied for a cerain user group, i is crucial for users employing differen rus represenaions o have a common undersanding abou he meaning of a given rus saemen. The conribuions of his paper are hree-fold: Firsly we presen he UniTEC generic rus model ha provides a common rus represenaion for he class of rus updae algorihms based on experiences. Secondly, we show how several well-known represenaive rus-updae algorihms can easily be plugged ino he UniTEC sysem, how he mappings beween he generic rus model and he algorihm-specific rus models are performed, and mos imporanly, how our absracion from algorihm-specific deails in he generic rus model enables users using differen algorihms o inerac wih each oher and o exchange rus saemens. Thirdly we presen he resuls of our comparaive evaluaion of various rus updae algorihms under a selecion of es scenarios. Inroducion The phenomenal growh of he Inerne ha we experienced during he las couple of decades, ogeher wih he fac ha compuers can be found no only in business environmens bu also in many households almos o he poin of being a commodiy nowadays, led o a widespread public accepance of his medium. There are pleny of reasons why people connec o he Inerne. Among he mos common usage scenarios are geing access o informaion, communicaing wih people and buying or selling goods. This is he personal version of he auhors. The final version, c Springer-Verlag, appears in he Proceedings of he Third Inernaional Conference on Trus Managemen (itrus25) available online via hp://www.springer.de/comp/lncs/index.hml.
There is no doub ha he Inerne offers masses of informaion in all kinds of differen areas, ranging from purely leisure-relevan possibly dispensable informaion, like who is currenly number one in he US-single-chars, o more criical areas, like produc reviews or even sock exchange daa. Especially in hese criical areas, he user needs correc informaion. Therefore he user needs o decide wheher he informaion provider is rusworhy or no. In real life, we use social nework srucures of friends, colleagues ec. o find rusworhy persons whom o ge advice or general informaion from. In he virual environmen of he Inerne, repuaion sysems model hese srucures up o a cerain degree supporing users in heir decision whom o rus and whom o avoid. The goal of hese sysems is o minimize he risk of ineracions wih srangers. One aspec, ha research in rus and repuaion sysems srives o deermine, is a suiable digial represenaion of rus, commonly referred o as a rus model. Tighly inerwoven wih rus models are he algorihms used o deermine, how his rus is updaed according o differen usually discree evens. Such evens migh be a new experience wih he person in quesion, or new informaion from oher rused sources regarding he repuaion of his person ec. Numerous differen models and rus updae algorihms have been proposed in he lieraure and each approach is paricularly well suied for a cerain user group or applicaion area. However, hese rus models are no ineroperable since here is a lack of a generic represenaion of rus. A generic rus model would allow users inending o use differen models o ranslae heir local represenaion o he generic one in order o undersand each oher s rus saemens. Our conribuion is buil on he observaion ha, alhough he algorihms used o compue a cerain rus value are quie differen from each oher, he daa ha he algorihms are working upon and he oucome of he algorihms are no ha differen and can hus be mapped on a generic model. We sugges one approach for such a generic represenaion which we implemened in he conex of he UniTEC disribued repuaion sysem. This generic rus model allows us o easily inegrae various exising rus updae algorihms. Anoher conribuion lies in a comparaive analysis of hese algorihms, which presens how he algorihms reac on various es scenarios. This has according o our knowledge no been done in his deph before. We srucure our paper as follows: In he nex secion we give a brief overview of he UniTEC repuaion sysem, in whose conex his research is being conduced. Afer discussing several general aspecs of rus and rus relaionships in Sec. 3 we presen in deail he componens of he generic rus model in Sec. 4. We inroduce in Sec. 5 a subse of rus updae algorihms implemened in UniTEC and he necessary adapaions. In Sec. 6 we describe several es scenarios ha he algorihms are subjeced o which is followed in Sec. 7 by a presenaion of he resuls of his evaluaion. We conclude our paper in Sec. 8.
2 Applicaion Area for a Generic Trus Model In his secion, we briefly poin ou he funcionaliy of he UniTEC sysem as one sample applicaion area for he inroduced generic rus model. UniTEC is a compleely decenralized repuaion sysem and consiss of a peer-o-peer nework of agens residing on nodes wih communicaion capabiliies. For privacy reasons, each user employs muliple virual ideniies or pseudonyms insead of his real ideniy when ineracing wih he UniTEC sysem. Each pseudonym has an associaed public and privae key pair and is responsible for one or more conex areas (see Sec. 3). The ideniy managemen componen allows o creae or remove pseudonyms and o assign conex area responsibiliies. The anonymous peer-o-peer (P2P) communicaion componen provides communicaion mechanisms beween pseudonyms while proecing he link beween real user ideniies and heir pseudonyms (see also []). UniTEC can sore and reques rused daa iems (TDI) abou arbirary producs or services. TDIs are recommendaions digially signed wih he key of he appropriae pseudonym and sored in he XML daabase of he daa managemen componen of he pseudonym owner s UniTEC agen. In order o rerieve a TDI, a requesing user poses a query o is own agen, which deermines from he query conex a neighborhood of already known pseudonyms deemed as capable of answering he query. The query is disseminaed hrough he means offered by he anonymous P2P communicaion componen o each neighborhood member and from here recursively furher. During he query disseminaion, a consruc called he rus chain is buil as par of he query, which consiss of a se of rus saemens, each specifying he rus of a node in is successor saring wih he original requeser. A node which has sored a TDI ha saisfies he query sends a TDI response o he requeser ha conains his TDI and he hen compleed rus chain. The rus managemen componen (TMC) evaluaes he rus chains conained in he TDI responses and presens o he requeser he TDIs ogeher wih he calculaed ransiive rus in he TDI-issuer. Furhermore, he TMC keeps rack of he user s rus in each pseudonym ha she or he has been in conac wih. More concreely, i sores rus in is daabase according o he specified rus model and updaes he rus in hese pseudonyms upon receip of user feedback regarding he qualiy of he received TDIs according o he rus updae algorihm specified in he user s preferences. This rus updae influences he neighborhood selecion he nex ime ha a query is received for he rus conex in quesion. A generic represenaion of rus is essenial especially for he rus saemens inside he rus chains o enable he requeser s TMC o compue he ransiive rus in each TDI-issuer independenly from he local rus models used a each inermediary. We are well aware of he fac, ha his brief inroducion leaves many quesions unanswered. For more in-deph informaion
regarding UniTEC, we would like o poin he ineresed reader o [2] and our projec websie. Afer having presened background informaion regarding he UniTEC repuaion sysem as a whole, we focus in he following on he capabiliies of is rus managemen componen TMC. We sar by inroducing our view on he various aspecs of a rus relaionship. 3 The Phenomenon of Trus Relaionships In order o undersand he phenomenon of rus relaionships, we firs need o undersand he meaning of rus. In he relaed work, various differen definiions of he erm rus have been proposed. One definiion popular in he agen field is from Diego Gambea [3] rus (or, symmerically, disrus) is a paricular level of he subjecive probabiliy wih which an agen assesses ha anoher agen or group of agens will perform a paricular acion.... We idenify wo relevan poins in his definiion: firsly, rus is used in order o predic an eniy s fuure behavior, secondly, rus is subjecive. The subjeciviy leads consequenly o asymmeric rus relaionships beween rusor, he eniy who is rusing, and rusee, he eniy who is rused. In he following, we idenify various dimensions of rus relaionships in addiion o rusor and rusee: Trus measure refers o he qualiy of he rus relaionship, which ranges from complee disrus over a neural rus measure o full rus. The more a rusee is rused, he higher he rus measure is supposed o be. Trus cerainy specifies he confidence of he rusor in his or her esimaion of he rusee. If his esimaion is gained via only few personal experiences or jus via word of mouh, he cerainy is supposed o be low. Trus conex People rus in a fine-grained manner depending on he area and goal in quesion, for insance person A migh rus person B o babysi her child whereas she migh no rus person B o repair a compuer. A conex can be represened by differen caegories as we described in [2]. Trus direcness Direc and indirec rus [4,5] represen wo disinc rus relaionships. Direc rus means ha he rusee can direcly cooperae wih he rusor. Wih indirec rus, he rusee is no supposed o cooperae direcly himself, bu should forward he cooperaion reques o a good exper. Consider for insance person A knowing ha person B has many friends working in he compuer business, alhough B is no schooled in his conex herself. A will no rus B direcly wih a repair ask bu migh very well rus recommendaions received indirecly via B from one of B s exper friends. Trus dynamics A rus relaionship is no saic, bu changes dynamically on various differen incidens, e.g. on own direc experiences. If for insance he babysiing of A s child by B wen well, he rus of A in B will increase. In addiion o own experiences, rus esimaions received from ohers influence he own rus assessmen as well. If A s good friends C, D, and E warn uniec.informaik.uni-sugar.de
A abou he unreliable naure of B, A migh refrain from relying on B s babysiing capabiliies. Lasly, quie ineresingly, rus relaionships may also change over ime when no experiences have been made, a fac, ha is up o our knowledge no covered in he relaed work ye. 4 Towards a Generic Trus Model Having presened he general conceps of rus relaionships in he previous secion, we describe in he following, how hese conceps are mapped on he componens of our generic rus model. The key componens of our model resul from an analysis of he characerisics of various exising rus models. 4. Trus Measure and Cerainy Various differen represenaions of rus values exis in he relaed work. Trus values can be depiced as real numbers in cerain inervals like for insance [, +], as done by Jonker and Treur [6] and Sabaer [7] or probabiliies in [, ], as proposed among ohers by Jøsang and Ismail [8], Yu and Singh [9], and Kinaeder and Rohermel [2]. Ohers propose discree values, like he binary represenaion by Blaze and Feigenbaum [] or four discree values inroduced by Abdul-Rahman and Hailes [5]. The meric used for he rus measure in our proposed generic rus model is a real number in he inerval of [, ]. Complee disrus is represened by whereas corresponds o full rus. This represenaion allows an easy ransformaion of any previously described measures in he generic measure as we will see in more deail in Sec. 5. No all invesigaed algorihms suppor he compuaion of a cerainy value, which saes he qualiy of he rus assessmen represened in he rus measure. If uncerainy is menioned [9,8,7] i is specified in he inerval [, ]. The rus cerainy in he generic rus model is represened similarly o he rus measure as a number in he inerval of [, ], whereas describes complee uncerainy and he oal cerainy. 4.2 Trus Conex As poined ou in he previous secion, applicaions can define various conex areas in which eniies can be rused. I is imporan o noe, ha hese areas are no necessarily independen from each oher. Differen kinds of dependencies can exis among he conex areas: insance-of relaionships are one-level relaionships for classificaion, is-a relaionships provide generalizaion, par-of relaionships enable aggregaion and surely many oher poenially applicaionspecific forms of dependencies beween conex areas can be imagined. For he sake of he rus model, however, we do no need o model all hese relaionships in deail. Insead, we model he asymmeric semanic disance beween he conex areas and herefore absrac from he kind of dependency.
The merics chosen for he semanic disance is a real number in he inerval of [, [. A disance close o represens a high dependency, a disance of refers o no dependency. Therefore, we organize he rus conex areas as a weighed direced graph as can be seen in. This allows us o spread he impac of a rus updae in one area o relaed areas. The conex areas and he semanic disances beween he areas are specified by he applicaions o be suppored wih rus managemen. However, due o he subjeciviy of rus, each user is enabled o locally modify he disances o sui his or her personal views...2 Vehicles Cars.75.8.7.5 Limousines Spors Cars.3. Mercedes CLK.8. Trucks Fig.. Example snippe of a weighed direced rus conex graph. The weighs represen sample semanic disance of he conex areas. 4.3 Trus Direcness Anoher dimension of a rus relaionship is is direcness. In our model, direc and indirec rus are wo disinc insances, each wih a specific rus measure, cerainy ec. They are sored and updaed separaely by he rus algorihms. 4.4 Trus Dynamics As already menioned in he inroducion, a change in rus occurs upon receip of feedback regarding an experience of a rusor wih a rusee. Various aspecs are discussed in he following ha influence he rus dynamics. Qualiy Feedback The rusor provides feedback abou he subjecive qualiy of a received informaion iem. The merics used o rae he qualiy is a real number in he inerval of [, ]. A perfec informaion iem is raed wih, describes a compleely unsaisfacory one. The generic rus model does no dicae how his feedback is gained; e.g. for recommendaions of a saic aribue-value srucure his feedback can be gained auomaically in a collaboraive filering syle. Trusor Confidence Trusors may specify a confidence in heir own offered informaion iems. This confidence is represened by a real number in he inerval of [, ]. Similar o he rus cerainy, sands for no confidence whereas sands
for he highes possible confidence in he offered informaion. This confidence influences he rus updae such ha a weak saemen wih a low confidence leads o only a sligh rus updae, wheher posiive or negaive. Transacion Uiliy Each informaion reques, and he corresponding responses and feedback saemens refers o a cerain ransacion he requeser or rusor is abou o ake. Depending on he ransacion s significance, he rusor specifies he uiliy as a real number in he inerval of [, ]. We assume, ha a maximum uiliy can be specified in such as uiliies higher as his maximum uiliy will lead o he same rus updae impac as wih he specified maximum uiliy. refers o he normalized maximum uiliy which leads o a rus updae wih a higher impac. Experience Aging (Opional) The qualiy of rusees is no necessarily consan bu may change over ime, for insance due o gahered experience in a cerain field. In order o deermine rus as a predicion of he fuure behavior, i is possible o specify, ha he laes experiences ough o weigh more han older experiences. We propose wo opions for experience aging: a feedback window and an experience aging facor. The feedback window limis he amoun of considered experiences, eiher depending on a cerain number of experiences or a cerain maximum age. The aging facor in he inerval of [, ] deermines he raio of a new experience o previous experiences in he updae compuaion. We describe in he following secion how his aging facor is used in he algorihms. Relaed Trus Conex Areas (Opional) As menioned before, an updae in a single rus conex area A may lead o an updae of a lesser exen in relaed areas B i according o he relaionships in he conex area graph. The semanic disance beween wo conex areas ha are linked via one or more inermediary areas can be compued by calculaing he produc of he semanic disances along he pah. The proporion of he updae of B i o A is deermined by he sronges semanic disance from A o B i, in oher words by calculaing he maximum produc of all pahs from A o B i. Conex area ha canno be reached from A or where he disance is no known are no updaed. Trus Fading (Opional) When no experience wih a rusee is made in a long ime, he old rus relaionship migh no longer be valid. This usually means ha he rus confidence level decreases over ime. Bu here migh be siuaions or ime frames when also he rus level decreases wihou new experiences. We represen he magniude of his fading effec wih a fading facor as a real number λ. A facor of means no fading effec. The higher he fading facor, he faser rus relaionship drops back o a sae specified by he rus algorihm. This sae migh be a sae of no rus and no confidence. 5 Suppored Algorihms and Necessary Adapaions The generic rus model presened in he previous secion was conceived in such a way ha exising rus models could be easily inegraed ino UniTEC. In he
following, we presen he mapping of he local rus models o he inroduced generic model and sugges some algorihmic adapaions. The subse of invesigaed algorihms discussed here are Abdul-Rahman Hailes, Bea Repuaion, ReGreT and he original UniTEC algorihm. Due o space consrains, our resuls on he work of Yu and Singh [9], heir previous suggesions [] and Lik Mui s algorihm [2] are no covered here. 5. Abdul-Rahman Hailes The work on a rus model in [5] is based on sociological sudies similar o he work of Marsh [3]. Here, inerpersonal rus is conex-dependen, subjecive and based on prior experiences. A repuaion informaion exchange amongs members of he communiy assiss on rus decisions. All hese aspecs fi well in our generic rus model. Trus is measured in a discree meric wih four values: very unrusworhy vu, unrusworhy u, rusworhy and very rusworhy v. Abdul-Rahman and Hailes describe hree uncerainy saes, which complemen he four rus values: more posiive experiences u +, more negaive experiences u, and equal amoun of posiive and negaive experiences u. Raings are specified in a discree meric: very bad vb, bad b, good g, very good vg. To fi his ino he generic rus model, he discree rus values have o be mapped ono he scalar rus meric. The range [, ] is spli ino hree equally sized ranges. The values a he borders of hese ranges represen he four values from he discree meric (, 3, 2 3, ). Each discree value is assigned a single posiion number (pos() = vu, pos() = u, pos(2) =, pos(3) = v). To map a value from he generic rus model ( g ) ono his discree meric ( d ), he following calculaion is applied: d = pos(round( g 3)). The same formulas are applied for mapping he four discree raing values. This ranslaion follows he reasoning ha rus in his model canno be greaer han very rusworhy, which is represened by he value of in he generic rus model. The semanics of he uncerainy values is no defined in [5], herefore he mapping ino our generic rus model is difficul. For he four rus values, no uncerainy is known, which is represened as a cerainy of in our generic rus model. The iniial rus value (when no previous experiences are known) is represened by he u uncerainy value, so i makes sense o keep he generic cerainy value of (he generic rus value is of no imporance in his case, so we also keep i a he lowes level of ). Rahman s paper does no give an explanaion on how o inerpre his uncerainy value in oher siuaions. The uncerainy values u + and u represen saes where slighly more posiive (or negaive) previous experiences have been recorded. This is expressed in our generic rus model by a sligh misrus (/3) or a small posiive rus (2/3). In hese cases he uncerainy componen is represened by a mean generic cerainy value (.5).
5.2 The Bea Repuaion Sysem The Bea Repuaion Sysem [8] is based on Bayesian probabiliy. The poseriori probabiliy of fuure posiive experience is represened as a bea disribuion based on pas experiences. The rus value, in his work called repuaion raing, is deermined by he expecaion value of he corresponding bea disribuion. This is a probabiliy value in he scalar range [, ]. A one-o-one mapping o our generic rus value is possible. The cerainy of he rus calculaion is defined in his paper by mapping he bea disribuion o an opinion, which describes beliefs abou he ruh of saemens ([4,5]). In his mapping he cerainy sars a and grows coninuously o wih more experiences being considered. This meric also can be direcly mapped o our scalar generic cerainy meric [, ]. Experiences in he Bea Repuaion Sysem are raed hrough wo values: r for posiive evidence and s for negaive evidence. The sum r + s represens he weigh of he experience iself. These wo weighed raing values can be mapped o he generic raing value ( R ) and he generic weighing meric ( w ) as r = w R and s = w ( R). In his rus model, he accumulaion of raings can make use of a forgeing facor, which is he equivalen o he generic aging facor. In he Bea Repuaion Sysem he forgeing facor (λ bea ) has a reversed meaning: λ bea = is equivalen of having no forgeing facor and λ bea = means a oal aging (only he las experience couns). Thus α = λ bea represens a simple mapping o our generic aging facor. 5.3 The ReGreT Sysem The ReGreT sysem [7] represens a repuaion sysem which uses direc experiences, winess repuaion and analysis of he social nework where he subjec is embedded o calculae rus. Direc experiences are recorded as a scalar meric in he range [, +]. Trus is calculaed as a weighed average of hese experiences and uses he same value range. A mapping o he generic values can be done by ransforming hese ranges o [, ] (shifing and scaling). A reliabiliy is calculaed for each rus value, based on he number of oucomes and he variaion of heir values. This reliabiliy is expressed as a value in he range [, ] which direcly maches he represenaion of our generic cerainy value. An aging facor is no used. Insead, he oldes experience is negleced (w = ), he newes experience is fully weighed (w = ). The weigh of experiences in beween grows linearly from o. 5.4 The Original UniTEC Algorihm In he firs work on UniTEC [2], a rus updae algorihm describes he rus dynamics. I calculaes a new rus value based on he old rus value and he new raing. Raings in he original UniTEC proposal are expressed as a binary meric of {, } (eiher bad or good experience). The rus updae algorihm
works as well wih raings in a scalar range of [, ] insead, which hen require no furher mapping o he raing merics of he generic rus model. In UniTEC we specified he cerainy of he rus asserion hrough a confidence vecor, where he amoun of direc and indirec experiences and a rail of he laes n direc experiences is recorded. A semanic inerpreaion of his vecor was no given. We need o calculae he cerainy as a single scalar meric as in he generic rus model. This can be accomplished in a similar manner as in he ReGreT Sysem, where he number of experiences and he variabiliy of is values are consolidaed ino a single value in he range [, ]. We creaed a simple fading algorihm ha works wih he UniTEC updae algorihm and uses he fading facor λ. In he ime when no experiences are recorded, rus will linearly drop o he minimal rus value in /λ ime unis. 6 Tes Scenarios To assess he qualiy of he rus updae algorihms presened in he previous secion, a series of es scenarios was developed. Each scenario simulaes a differen behavior paern of rusor and rusee as a lis of raings. This paern is hen refleced by each single rus algorihm as rus dynamics. A es scenario can bring forward a specific feaure or a malfuncion of a rus updae algorihm. As he es scenarios simulae he behavior of real-world people, here are cerain expecaions associaed wih he rus dynamics. A rus algorihm is expeced o generae rus dynamics ha saisfy hese expecaions. Failing o comply wih he specified expecaions can eiher be a consequence of he calculaions hemselves or i reflecs a shorcoming of he adapaions and mappings necessary for he local rus model o work in he generic rus model. We wan o sress he fac, ha due o he subjeciveness of rus in general, also he qualiy esimaion of he behavior refleced in he rus dynamics is subjecive. Therefore, we do no offer a ranking of rus updae algorihms, bu insead poin ou he disincive feaures of he algorihms, so ha each user can choose he algorihm ha mos closely reflecs his own expeced behavior. OnlyMaximalRaings Saring from he iniial rus sae, only maximal raings (= ) are given. We would expec he rus o grow coninuously and approach he maximal rus value (= ). OnlyMinimalRaings Saring from he iniial rus, only minimal raings (= ) are given. If he iniial rus is he minimal rus value (= ), hen rus should say a his level. Oherwise, we would expec he rus value o decrease and evenually approach he minimal rus value. MinimalThenMaximalRaings Firs, a series of minimal raings is given, which is followed by a series of maximal raings. We would expec he rus dynamics o sar as described in he es scenario OnlyMinimalRaings. Afer swiching o maximal raings, rus should rise again. The expeced growh rae of rus afer he sar of he maximal raings should be lower han in he OnlyMaximalRaings es scenario.
MaximalThenMinimalRaings Firs, a series of maximal raings is given, followed by a series of minimal raings. We expec rus o rise as in he es scenario OnlyMaximalRaings. When he series of minimal raings sars, rus should decrease again. The rus decrease rae in he second half of he es should be slower han in he es scenario OnlyMinimalRaings. SpecificRaings Afer he previous es scenarios, which work wih exreme raings, hese four es scenarios make use of a specific se of raings (he SpecificRaings) which simulae a real-world raing siuaion. The raings are:.,.8,.5,.4,.5,.,.6,.7,.7,.8,.,.4,.3,.2,.2,.5,.,.3,.4,.3. These raings are submied in his original order (-Normal), in a reversed order (-Reversed), ordered by ascending (-OrderedAsc) and by descending raing value (-OrderedDesc). In he Normal order, here are more posiive raings in he firs half of he raing sequence, whereas negaive raings predominae in he second half. The expecaion is ha he final rus value is slighly below he mean rus value (=.5). Wih he Reversed order he expecaion for he final rus value is a value slighly above he mean rus value. If he ending rus values in all four scenarios are equal, i suggess ha he rus algorihm uses an indisinguishable pas (see [6]), which means ha he order of previous experiences does no maer. This should no he case when using an aging facor. KeepPosiive This scenario has a dynamic naure, in ha i acively reacs on he resuling rus values afer each individual raing. Maximal raings are given unil a cerain level of rus is reached (>.8). This rus level is hen misused in form of minimal raings, unil he rus value reaches a misrus level (<.5). Then, maximal raings are submied o raise rus again. This process is repeaed four imes. Here he rus algorihm s reacion o aemps of misuse is analyzed. We would expec rus o quickly drop o a misrus level when he minimal raings occur. The opimal algorihm should quickly deec his misuse aemp and reac appropriaely, e.g. by reporing minimal rus or even blacklising he user. 7 Evaluaion We subjeced each rus updae algorihm discussed in Sec. 5 wih a variaion of aging facors o each es scenario from he previous secion. For each evaluaion graph we use he represenaion of he algorihms presened in Fig. 2. Raings BeaRepuaion BeaRepuaion aging=.3 Rahman ReGreT UniTEC aging=.3 Fig. 2. Key for he rus dynamics presened in he evaluaion.
Tes scenario OnlyMaximalRaings presened in Fig. 3 illusraes he differen iniial rus values of he algorihms: The rus dynamics sar eiher wih a rus value of (UniTEC and Abdul-Rahman) or.5 (Bea Repuaion and ReGreT). Trus rises monoonously for all algorihms. Trus in Bea Repuaion wih no aging facor and UniTEC approaches asympoically he maximum rus value. Bea Repuaion wih an aging facor approaches a cerain level of posiive rus value. ReGreT and Abdul-Rahman reach maximum rus afer jus one maximal raing and remain a his level. Similar effecs can be noiced in he es scenario OnlyMinimalRaings (see Fig. 4). The rus algorihms ha sared wih he lowes rus value (UniTEC and Abdul-Rahman) say a his minimum rus level. ReGreT ha sared a.5 drops o he lowes rus value afer jus one bad experience. Bea Repuaion also sared wih a rus value of.5. Wihou aging facor, rus approaches asympoically he minimum rus value. Wih an aging facor, rus never drops below a cerain level of misrus.,8,6,4,8,6,4 Fig. 3. OnlyMaximalRaings Fig. 4. OnlyMinimalRaings Bea Repuaion wih an aging facor uses only a limied inerval of he oally available rus value scope. This happens because he accumulaion of he evidence (r and s) using a posiive aging facor represens a geomeric series. An upper limi for r and s hus limis he possibly reachable maximum and minimum rus values. One possible soluion o make use of he whole range regardless of an aging facor is o scale he possible oupu range o he whole generic rus value range. This can only be done if he aging facor remains consan hroughou he relevan raing hisory. In MinimalThenMaximalRaings (Fig. 5) when he maximal raings sar, rus sars rising again in all analyzed algorihms bu Abdul-Rahman s. In his laer case, rus remains a he lowes level unil as much maximal raings as minimal raings have been received. The discree merics of his rus model does no suppor oher inermediae saes. Anoher ineresing observaion is ha UniTEC shows he same rise on rus as in he OnlyMaximalRaings es scenario (rising above.8 afer 5 maximum raings). The oher algorihms show a slower rise of rus, as we would expec afer he negaive impac of he negaive raings. This demonsraes one deficiency of algorihms like he original UniTEC one,
which rely solely on he las rus value and he new raing for heir calculaions and do no consider adequaely he remaining hisory of raings. The MaximalThenMinimalRaings es scenario (Fig. 6) shows similar resuls as he previous scenario. I sars as expeced like he OnlyMaximalRaings. When he minimal raings sar, rus drops wih all bu Abdul-Rahman s algorihm. Here, rus suddenly drops from maximum o he minimal value a he end of he scenario which is he poin when more minimal han maximal raings are recorded in he hisory. In boh scenarios we noice ha Bea Repuaion wihou an aging facor shows a slow reacion o he paern change in he raings.,8,6,4,8,6,4 Fig. 5. MinimalThenMaximal Fig. 6. MaximalThenMinimal The SpecificRaings es scenarios are depiced in Figs. 7, 8, 9 and. In SpecificRaingsNormal mos algorihms follow he expeced rus dynamics. The ending rus value for UniTEC and Bea Repuaion wih aging facor of.3 is jus below he average rus value of.5. ReGreT and Bea Repuaion wihou an aging facor are a bi more opimisic ending jus above.5. In SpecificRaingsReversed he opposie can be seen: The ending rus value is jus above he rus value mark of.5. In hose four es scenarios Abdul-Rahman generaes a rus dynamic ha follows our expecaions up unil he end, when suddenly rus and cerainy drop back o he lowes values. Wha happened here is ha he algorihm reached he uncerainy sae u. The mos eviden problem wih his can be seen in Fig. 9. A he las couple of raings his sae of uncerainy is reached, which is no expeced a all. The weakness lies in he lack of semanical meaning of he u sae. The only soluion would be o aler he original algorihm and is underlying rus model o improve he way uncerainy is handled. We see he characerisic of indisinguishable pas wih Abdul-Rahman and Bea Repuaion wihou an aging facor: The ending rus values are he same regardless of he ordering of he raings. All remaining algorihms use aging of raings, leading o differen ending values depending on he order of he raings. In our las es scenario, KeepPosiive, he raing hisory depends on he calculaed rus values. In Fig. he reacion of he Bea Repuaion algorihm o he scenario shows ha he use of an aging facor helps wih a fas reacion
,8,6,4,8,6,4 Fig. 7. SpecificRaingsNormal Fig. 8. SpecificRaingsReverse,8,6,4,8,6,4 Fig. 9. SpecificOrderedAsc Fig.. SpecificOrderedDesc o he sudden minimum raings, while i also makes he reacion speed more independen of he oal hisory size. I can be noiced ha wihou an aging facor, he dynamics of rus ges more seady as he hisory of raings grows. The reacion of he remaining algorihms o his es scenario can be seen in Fig. 2. Abdul-Rahman canno really compee due o he lack of precision: Afer jus one maximum or minimum raing rus flips from minimum o maximum and back o minimum rus value. ReGreT shows a similar deficiency as Bea Repuaion wihou an aging facor: As more experiences are recorded, rus dynamics reac slower o raing paern changes. UniTEC shows quick reacion o he minimum raings while mainaining his reacion independenly of he hisory size.,8,6,4,8,6,4 Fig.. KeepPosiive and Bea Repuaion Fig. 2. KeepPosiive and he oher algorihms
8 Conclusion In his work we invesigaed he various dimensions of rus relaionships. Furhermore, we presened our approach owards a generic rus model which represens hese dimensions and includes measures for rus, cerainy, experiences and facors required for rus calculaions. The model is based on observaions gained hrough he analysis of a se of well-known rus models from he lieraure. I is generic in ha i allows o plug in differen specialized models and rus updae algorihms and provides a bijecive mapping beween each local model and he generic rus represenaion. We discussed our adapaions of he original models which were necessary because we considered new rus relaionship dimensions and ones ha are no suppored as such by all algorihms. This generic rus model provides for he firs ime he possibiliy o compare various rus updae algorihms hrough is common represenaion of algorihm inpus and oupus. We developed a se of es scenarios o assess he subjecive qualiy of each suppored algorihm. Our evaluaion poins ou several imporan qualiies bu also deficiencies of he algorihms. To summarize our findings, we conclude ha he Abdul-Rahman Hailes algorihm in our generic rus model suffers from is discree four sep merics in comparison o he field. The Bea Repuaion sysem wih an aging facor provides in our view he bes overall resuls. The only drawback is he limiaion of he rus value bandwidh which is proporional o he aging facor. The ReGreT algorihm provides responses o our es scenarios ha mee our expecaions, bu is dynamics proved o be highly dependen on he hisory size: Too fas reacions wihou or wih a small previous hisory of experiences, and slower dynamics as more experiences were colleced. Finally he original UniTEC proposal provided a simple ye efficien algorihm and eased inegraion of he various dynamics. However, a deficiency of his algorihm lies in focusing merely on he curren rus value and he laes experience and no aking ino accoun paerns of pas experiences. Fuure work on rus updae algorihms could consider giving more weigh o negaive experiences as opposed o posiive ones. Furhermore, analyzing paerns of pas experiences would be anoher ineresing aspec o beer deec misuse aemps and enhance he calculaion of rus cerainy. Besides improving exising rus updae algorihms, we plan o invesigae how o fi furher algorihms ino he generic model. Regarding he farher fuure, we consider o refine he represenaion of semanic disance in he model. In he curren sae of UniTEC, he semanic disances beween he differen rus conex areas are specified by he applicaions and can be modified by each user. I would be challenging bu surely ineresing o invesigae, wheher and if yes how his process could be auomaed furher. References. Kinaeder, M., Terdic, R., Rohermel, K.: Srong Pseudonymous Communicaion for Peer-o-Peer Repuaion Sysems. In: Proceedings of he ACM Symposium on Applied Compuing 25, Sana Fe, New Mexico, USA, ACM (25)
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